Piecewise Chebyshevian Splines: Interpolation versus Design

International audienceWe consider the wide class of all piecewise Chebyshevian splines with connection matricesat the knots. We prove that a spline space of this class is “good for interpolation” if and only ifthe spline space obtained by integration is “good for design”. As a consequence, this providesus with a simple practical description of all such spline spaces which can be used for solvingHermite interpolation problems. These results strongly rely on the properties of blossoms